周期轨道的量子化与量子能谱中的长程关联

用二维可积系统的半经典量子化方案和二维无关联振子系统的量子能级与周期轨道之间的对应关系,讨论了一组量子能级之间具有长程关联的内在机制,在二维无关联振子系统中,发现了具有相同拓扑M(M1,M2)的周期轨道相对应的量子能级之间存在着长程关联,并以二维4次无关联振子系统为例做了具体说明.     

一类两个指标的非常系数齐次递推式之解

给出了两个指标的非常系数齐次递堆式的显式解．该解为其系数与初始值的显函数．它为求解组合计数中的有关问题，直接提供了一个具体的计算公式．     

The density function of the number of moves to complete the Towers of Hanoi puzzle

Any sequence of legal moves leads the Towers of Hanoi puzzle to an arrangement from which the final configuration must be built up. A recursive algorithm which finishes off the puzzle is considered and, assuming a uniform distribution on the possible unfinished situations, the density function of the number of moves it takes is derived.     

双变量部分theta函数的乘积公式与性质

本文研究一类新的双变量部分theta函数,它是经典部分theta函数的推广,主要围绕这类函数的乘积公式、递推关系、级数展开等性质展开讨论.作为主要结果,我们建立了任意两个双变量部分theta函数的乘积公式,推广了Andrews-Warnaar经典部分theta函数的乘积公式,发现了双变量部分theta函数所满足的二阶递...     

基于Copula函数的华南台风灾情重现期研究

利用1981-2014年华南台风灾情数据,选取受灾人口、农作物受灾面积和直接经济损失,应用Copula函数理论,计算灾情重现期,分析台风灾害的灾情.首先,借助Clayton Copula函数构造三变量的联合分布,计算单变量重现期、联合重现期及同现重现期,并求出该重现期下的设计值.计算结果表明联合重现期的设计值要优于单变量重现期和同现重现期的设计值．因此,选取联合重现期的设计值作为防灾标准的最优参考,并将联合重现期记为灾情重现期．然后,计算2015-2017年登陆华南台风灾害的灾情重现期,并对台风灾害的灾情进行分析．发现台风灾情重现期越长的台风造成的灾情越严重．最后,利用灾情重现期与致灾重现期对台风灾害的发生频率作综合性分析,可以为台风灾害的风险评估提供一种新思路．     

Laguerre-Freud equations for Generalized Hahn polynomials of type I

We derive a system of difference equations satisfied by the three-term recurrence coefficients of some families of discrete orthogonal polynomials.     

半直线上的独立随机环境中可逗留的随机游动

主要研究了在随机环境独立的情况下,右半直线上随机环境中可逗留的随机游动的常返性和非常返性.     

The analytic solution for the power series expansion of Heun function

The Heun function generalizes all well-known special functions such as Spheroidal Wave, Lame, Mathieu, and hypergeometric ₂F₁${}_2{F}_1$, ₁F₁${}_1{F}_1$ and ₀F₁${}_0{F}_1$ functions. Heun functions are applicable to diverse areas such as theory of black holes, lattice systems in statistical mechanics, solution of the Schrödinger equation of quantum mechanics, and addition of three quantum spins.     

On the number of hypercubic bipartitions of an integer

For n≤2^k$n\le 2^k$ we study the maximum number of edges of an induced subgraph on n$n$ vertices of the k$k$-dimensional hypercube _Qk$Q_k$. In the process we revisit a well-known divide-and-conquer maximin recurrence f(n)=max(min(_n1,_n2)+f(_n1)+f(_n2))$f\left(n\right)=max(min(n_1,n_2)+f\left(n_1\right)+f\left(n_2\right))$ where the maximum is taken over all proper bipartitions n=_n1+_n2$n=n_1+n_2$. We first use known results to present a characterization of those bipartitions n=_n1+_n2$n=n_1+n_2$ that yield the maximum f(n)=min(_n1,_n2)+f(_n1)+f(_n2)$f\left(n\right)=min(n_1,n_2)+f\left(n_1\right)+f\left(n_2\right)$. Then we use this characterization to present the main result of this article, namely, for a given n∈N$n\in \mathbb{N}$, the determination of the number h(n)$h\left(n\right)$ of these bipartitions that yield the said maximum f(n)$f\left(n\right)$. We present recursive formulae for h(n)$h\left(n\right)$, a generating function h(x)$h\left(x\right)$, and an explicit formula for h(n)$h\left(n\right)$ in terms of a special representation of n$n$.